Lots of continuity errors with the episode order and the like
I kind of wonder what was going on...whether Nickelodeon aired them out of order, or whether the writers changed their mind on what they were going to do in the big picture.
The first instance (that I recall) is in season 2's Doug vs. the Klotzoid Zombies. At the end, it is revealed they are throwing him a "1 year anniversary party." This is impossible, unless this episode was supposed to have taken place at the end of the series chronologically...even then, it wouldn't make sense, as they were leaving Bluffington Elementary as they were doing it.
That was a true "WTF?" moment given that one of the central features of the character of Doug is that he's in 6th grade, and unless they had arrived at a decision he was now in junior high, it would make no sense to say a year had elapsed.
Later in season 2, when Judy directs the school play, Skeeter makes a reference to her performance in season 1, saying "maybe they liked her so much last year they invited her to come back." Again...what was going through the minds of the writers on that one, I don't know.
It seems the writers had "we're doing season 2" stuck in their head, and they weren't thinking about the fact that it's not YEAR 2 for Doug if he's in the same class.
Kind of gives new meaning to Roger's "I've been in the 6th grade for 3 long years" line in Doug Graduates.
In season 3, I believe the episodes with Mr. Shelacki were aired out of originally-intended chronological order based on Beebee's exclamation, "that's the guidance counselor!" in Doug's New Teacher, which we were already aware of thanks to the order they aired. Not really a big deal there, but it's worth noting what was probably originally intended. That one's on Nickelodeon, but it doesn't really matter, as the exclamation is irrelevant and was only intended for the benefit of the audience. We just didn't need it.
Then comes Doug Is Hamburger Boy...the "laughing at Mr. Dink all that time" line when he learned Mr. Dink was the Hamburger Boy during past summers doesn't seem nearly as troubling to me as the fact that it's supposedly summer vacation in the first place. This is late season 3...Doug doesn't graduate until the end of season 4, and the very next thing that happens after his graduation is the story that is paired with it - Doug's Bad Trip. This episode began with a reference to the first day of summer vacation, so it would have to be sandwiched in between Doug Graduates and Doug's Bad Trip chronologically. And in season 4, he's back in the same 6th grade class, winding everything down...even though there appeared to be a couple of summer-themed episodes (such as Doug Tips the Scales, with Beebee's pool party), though I'm not sure it was ever explicitly stated it was summer vacation in those, and if not, then it could just be May/June as they wind down and it's hot outside.
My solution with Doug Is Hamburger Boy is simply to think of it is a fantasy Doug wrote about or dreamed, given the other continuity error with nobody knowing how to swim in it, plus general "surreal" feeling to the episode.